Vane-type rotary fluid-displacing machine

ABSTRACT

A fluid-displacing machine has a rotor member and a stator member relatively rotatable about a common axis. One of the members has an internal peripheral profile that is sinuous, opposed to which the other of the members has a peripheral profile that is circular. The contour of the sinuous profile generates an odd number of evenly spaced chambers interposed by cam surfaces and is developed so that the diametral distance between its opposite profile surfaces is constant. At least one diametrally disposed vane is slidably mounted in the circular member and adapted to continuously contact and sweep the sinuous profile surface of the other member, there being inlet and discharge passages leading into and out of each chamber respectively whereby upon relative rotation of the members pumping and/or compressing action is promoted. Subordinately, novel sealing means between the vane and the sinuous profile, and pressure-assisted sealing and automatic wear takeup means for the relatively moving lateral surfaces of the machine, are provided. Disclosed also is a mathematical formula for developing the contour of the sinuous profile.

3 United States Patent 1151 3,642,390

Ostberg 1 Feb. 15, 1972 [54] VANE-TYPE ROTARY F LUID- 2,985,110 5/1961 Burt et a]. ..l03/l2l DISPLACING MACHINE 3,232,237 2/1966 Burt 3,251,308 5/1966 Dugan ..103/l21 [72] Inventor: Bernhard Nils Ostberg, Temple St.,

Heyfield, vlctona, Austral"! Primary Examiner-Carlton R. Croyle 22 Filed: Sept 8, 19 9 Assistant Examiner-John .1. Vrablik Attorney-Sommers & Young [21] Appl. No.: 855,996

[57] ABSTRACT [30] F reign Application Priority Data A fluid-displacing machine has a rotor member and a stator Sept 12 1968 Australia 43 288/68 member relatively rotatable about a common axis. One of the members has an internal peripheral profile that is sinuous, op- Nov. 8, 1968 Australia ..46,002/68 posed to which the other of the members hasva Peripheral profile that is circular. The contour of the sinuous profile [52] us Cl tai generates an odd number of evenly spaced chambers inter- [51] Int Cl 2 3/00 6 5 6 5/00 posed by cam surfaces and is developed so that the diametral 58] Fie'ld 418/133 150 156 175, distance between its opposite profile surfaces is constant. At 103/121 153- 9i/74 129 123 1 least one diametrally disposed vane is slidably mounted in the 8 circular member and adapted to continuously contact and sweep the sinuous profile surface of the other member, there being inlet and discharge passages leading into and out of each [56] Reerences cued chamber respectively whereby upon relative rotation of the UNITED STATES PATENTS members pumping and/or compressing action is promoted.

1 496 222 6/1924 Hill .230/141 A shherdihetely, hovel Sealing means between the vane end the 1,977 780 10,1934 stage g "103,137 sinuous profile, and pressure-assisted sealing and automatic 212471410 7/1941 Ross ..91/129 wear takehP means the relatively meving lateral Surfaces 2,318,346 5/1943 Wakefield ..l03/l37 eflhe maehme are Previded- 217301076 1956 Hogue 103/121 Disclosed also is a mathematical formula for developing the 2,840,991 7/1958 Nisbet 103/123 t fth sinuous fil 2,845,872 8/1958 Farron et al. ..l03/l23 2,853,023 9/1958 English 103/ 1 36 12 Claims, 12 Drawing Figures l l l l 1 2 V/Y/Vlf) Y /7/ A 22 4' 2e 1e 2s &-

PATENTEDFEBISIQTZ "3,542,390

' sum 1 u? 8 FIGURE 2 PAIENTEDFEB 15 I972 I SHEET 3 [IF 8 PAIENTEDFEB 15 1972 3.6%.390

sum 8 0r 8 PATENTEBFEB 15 I972 SHEET 7 BF 8 wdDuI VANE-TYPE ROTARY FLUID-DISPLACING MACHINE This invention relates to vane-type rotary fluid displacing machines, such as pumps and compressors, and has for its principal objective a machine of simple construction in which the rotor member and stator member are relatively rotatable about a common axis, either member being stationary and the other rotatable.

A subordinate objective is to provide a novel sealing device between the relatively moving contact surfaces of one said member and the vane or vanes carried by the other said member, which device also contributes to simplifying the manufacture of the machine.

It is inherent in the invention that either the rotor rotates in the stator casing in the normal manner, or the inner member (normally the rotor) may remain stationary and the casing rotate, with advantages further elaborated hereinafter.

With the above-stated principal objective in view, the invention provides a vane-type rotary fluid displacing machine comprising an external member cooperating with an internal member, the members being relatively rotatable about a common axis, the external member having an internal peripheral surface and the internal member having an external peripheral surface, the surfaces being opposed, one of which peripheral surfaces has a sinuous profile developed so that the diametral distance between its opposite profile surfaces is constant, the other peripheral surface being circular, said surfaces defining between them a plurality of an odd number of evenly spaced chambers interposed by cam surfaces, at least one diametrally disposed vane slidably mounted in the circular member and adapted to continuously contact and sweep the profile surface of the other member, so that upon relative rotation of the members the or each vane slides in the circular member as the vane follows the profile surface, and inlet and discharge passages leading into and out of each chamber respectively, whereby fluid is alternately drawn into and discharged from the chambers by the sweeping action of the vane or vanes.

In one form of the invention the external member, or casing, has an internal peripheral surface following a sinuous profile defining a plurality of an odd number of evenly spaced outwardly extending chambers interposed by inwardly extending cam surfaces, the internal member being circular and having at least one diametrally disposed vane slidably mounted therein and adapted to continuously contact and sweep the casing profile.

In another form of the invention the external member, or casing, has a circular internal peripheral surface while the internal member has an external peripheral surface following a sinuous profile defining a plurality of an odd number ofevenly spaced inwardly extending chambers interposed by outwardly extending cam surfaces, there being preferably two diametrally opposed vanes slidably mounted in the casing. In this arrangement the two vanes would be rigidly connected so that they operate in unison.

In the former arrangement, a single diametrally disposed vane located in the internal member may be employed. In either case the contour of the profile surface will be such that the diametral distance between the opposite profile surface, i.e., the surfaces contacted by the vane or vanes, is constant.

FIGS. 1, 2, 3 and 4 illustrate the mathematical development of the contour of the profile surface of the device of the present application;

FIG. 5 is a sectional elevation, taken along the line 55 of FIG. 6, of a basic form of pump or compressor, according to the invention;

FIG. 6 is a sectional elevation taken along the line 6-6 of FIG. 5;

FIG. 7 is a sectional elevation taken along the line 77 of FIG. 8, ofa modified form of the machine;

FIG. 8 is a sectional elevation, taken on the line 88 of FIG. 7;

FIG. 9 is an end elevation of a modified form of casing body;

FIG. 10 is a sectional view, taken on the line 10--10 of FIG. 9; and

FIGS. 11 and 12 indicate a further embodiment of the invention of the present application.

In one example, the contour of the profile surface may be developed according to the following mathematical formula, having reference to the accompanying diagrams designated FIG. 1, FIG. 2, FIG. 3 and FIG. 4:

Where FIG. 1 illustrates the development of a sinuous profile for one of the movable members of the present apparatus, FIG. 2 illustrates the trigonometric relationship of two points of the profile of FIG. 1, FIG. 3 illustrates a portion of the sinuous profile of FIG. 1, a second portion of a sinuous profile corrected for curvature of the vane of the present ap paratus, and a third curve shows a portion of a sinuous profile corrected for a liner to be placed inside the sinuous profile, and FIG. 4 shows an enlarged portion of FIG. 3.

Consider a point P,, performing three simple harmonic motions while at the same time rotating in a complete circle. This point then describes a curve similar to that shown in broken line in FIG. 1. This is curve 1. Let this point P also be the center of curvature of a surface the periphery of which moves in unison with point P This surface will describe a similar but not parallel curve to curve 1. This is called curve 2. A curve parallel to curve 2 and separate from it by a finite distance is called curve 3. (FIG. 3).

P actually represents the center of curvature of the vane end. Curve 3 described the shape of the contoured surface of the pump housing.

ln practise by using the subsequent formulas and with the assistance of a computer we obtain values for points of curve 1. These values are fed into a numerical control milling machine and a template cut. From this template using a contour milling machine and adjusting our mills to the radius of curvature of the vane and we obtain a milled contour conforming to curve 2. If we add to the radius of the mill the thickness of the liner, making the total radius the (R+t)'of the later formulas then we obtain a contour conforming to curve 3.

DERIVATION OF FORMULAS Let r be the radius vector defining the position of P the center of curvature of the vane end.

b radial distance from center of rotation to mean position ofS.H.M. (simple harmonic motion) of P a radial distance to nearest point of S.H.M. 0, deflection of rotating radius from point of maximum deflection of S.H.M. R radius of curvature of vane end. I distance separating curve 2 and curve 3. The broken line (FIG. 1) indicates the curve drawn by point P,, performing three S.H.M.s while rotating in one complete circle.

DIAGRAM FIG. A

Consider point P,, as commencing its motion at J. As it rotates an angle 0, from the datum line about 0 the point N- whose projection on the radius vector defines the S.H.M.- rotates through an angle r =0P =0S+SN sin (319 -90) or DIAGRAM FIG. 2

Let the point P,, on the curve in FIG. 1 move a small distance to P Then 0L=r, cos ---r LP,,=r sin 60=r,60(60 being in radians) tan a=LP,,/LP, =r,66/8r, as 50 becomes smaller a= Substituting vaues for tin/d we obtain 4 DIAGRAMS FIGS. 3 AND 4 Curve 1 is traced out by center of curvature of vane end.

Curve 2 is traced out by curved surface of vane end.

Curve 3 is curve to be formed to allow for liner.

5 is the angle between the radius vector and the tangent. Line P,P P is at right angles to the tangent of each of the three curves.

Applying the cosine rule.

Again applying the cosine rule.

substituting values for r r and R in this equation we get the value of 8 The formula for any curve parallel to this curve and separated from it by a distance oft is given by substituting R?! for R. r now becomes radius vector r (not shown) and angle 6 becomes 0;, (not shown) thus defining the shape into which the liner ofthickness I fits.

Considering now the internal circular member arrangement, single diametral vane construction is preferred for simplicity. This "single" vane may be in two radially extending portions stressed apart by resilient means to that the profilecontacting edges of the vane portions are constantly pressed against the profile surface to improve sealing.

In one form of this construction the inwardly directed ends of the two portions of the vane are provided with interacting ratchetlike means whereby the composite vane can be extended lengthwise when in situ until the outwardly directed ends operatively contact the casing profile surface, the ratchet like means then preventing reversal of this movement so that the length of the vane is maintained independently of the resilient means.

Additional sealing means. such as inlays of plastic material, may be employed at contact edges in known manner.

lt is a subordinate feature of the invention to provide a novel sealing device between the casing profile surface and the vane, which sealing device comprises a thin liner of resilient sheet material located within the casing adjacent the profile surface and conforming to the contour of the profile, the liner being separated from the profile face by a layer of elastic material, such as crepe rubber or plastic. Where very high temperatures are involved, this layer could be composed of asbestos.

Preferably the circular member. has a flange at one or each side and the separating elastic layer in the profiled member is stressed laterally against the relatively moving surfaces of said flange or flanges, thus providing a seal along the sinuous It is well recognized in the art that in vane-type rotary machines having a rotary vane-carrier, the centrifugal component acting upon the vane or vanes can create a serious problem, especially at speed, and at very high speeds can be prohibitive.

As mentioned before, it is inherent in the instant invention that the, internal vane-carrying member can remain stationary, while the external casing (which carries no vanes) can rotate, thus entirely eliminating this problem. The common axis of the casing and the internal member further simplifies this arrangement.

lnlet and outlet fluid ducts can, with simplicity, be via hollow central coaligned shafts supporting the internal member at each end, which member is stationary in this arrangement.

A pump or compressor according to the invention provides a simple valveless construction in which the direction of fluid flow through the machine is automatically reversed merely by reversing the direction of machine rotation.

A subordinate feature of the present invention is the provision ofa novel sealing means for the relatively moving lateral surfaces of the machine.

The effective sealing of these lateral surfaces, especially after wear has taken place, has always presented a problem, as leakage in this region greatly reduces the operating efficiency of the machine.

The primary objective in endeavours to solve this problem has been a device that will automatically take up or accommodate lateral wear as it occurs.

A further desideratum is a device that will automatically increase the contact pressure between these relatively moving lateral surfaces with increase in the working pressure of the machine.

The said subordinate feature provides, in a rotary fluid-displacement machine according to the invention having an outer casing including a body portion and two primary end walls rigid with said body portion, and an internal member operating within said casing, said member and said casing being relatively rotatable, the characteristic of sealing means for the relatively moving lateral surfaces of the machine, said sealing means comprising a secondary end wall disposed against or integral with one lateral surface of said member and defining a space between said secondary end wall and one of said primary end walls, the member and secondary end wall having limited freedom of axial movement within said casing, said space being utilized to apply fluid pressure to the space side of said secondary end wall to press it against the member thereby pressing the member against the other one of the primary end walls to provide a pressure-assisted seal at said lateral surfaces.

(In this specification it is to be understood that, where the internal member is said to have axial movement within the casing, this also covers the instance of the casing being axially movable with respect to a stationary internal member.)

In a preferred arrangement the fluid pressure generated by the machine is employed to provide fluid pressure-assisted sealing and this is conveniently achieved by ducting affording fluid communication between the space and the pressure side of the machine.

In one practical application of this subordinate invention the internal member is stationary and the outer casing rotates upon bearings integral with the primary end walls and journaled on the stationary shafts extending axially at each end of the internal member. The casing has limited axial freedom to float" on he internal member so that the lateral surfaces can make sealing contact under fluid pressure in operation.

Preferably the secondary end wall is disposed on the discharge (pressure) side of the internal member and attached to or integral with the lateral surface of the member on that side thereof. It may be in the form ofa peripheral flange.

The periphery of the secondary end wall or flange extends into and in sliding engagement with a concentric circumferential recess formed in the interior periphery of the casing body. This recess provides a degree of axial freedom from the casing to allow of the pressure-assisted action as previously explained.

There is an annular space or chamber between the secondary end wall and the adjacent primary end wall, and this space is in communication with the pressure fluid on the discharge side of the machine. The annular space is also in communication with the outlet end of the hollow shaft, such communication being conveniently achieved by a hole, or holes, drilled through the shaft into its hollow interior and registering with the annular space.

The area of the secondary end wall which is subjected to hydrostatic pressure on the space side is considerably greater than the area thereof exposed to fluid pressure on the vane side (working side), since the greater part of the lateral area 7 on the vane side is taken up by the internal member carrying the vane, so that in operation the combined internal member and secondary end wall act as a differential piston axially slidable in the cylinderlike casing.

In the present instance the casing is free to move axially in the stationary internal member so that the differential hydrostatic pressure acts to press the primary end wall at the inlet side of the machine continuously against the adjacent lateral surface of the internal member, thereby effecting a pressure contact seal between these lateral surfaces irrespective of any wear that may take place in this region.

It will be plain to those skilled in the art that, in the arrangement above described, a further advantage obtains, viz the greater the pressure generated by the machine, the greater will be the differential hydrostatic pressure operable to provide an effective seal.

Practical arrangements of the invention will now be described with reference to the accompanying drawings, in which FIG. 5 is a sectional elevation, taken on the line 5-5 of FIG. 6, of a basic form of pump or compressor, according to the invention,

FIG. 6 is a sectional elevation taken on the line 66 of FIG.

FIG. 7 is a sectional elevation, taken on the line 7-7 of FIG. 8, ofa modified form of the machine,

FIG. 8 is a sectional elevation, taken on the line 88 of FIG. 7,

FIG. 9 is an end elevation ofa modified form of easing body,

FIG. 10 is a sectional view, taken on the line 10-10 of FIG. 9.

Referring now to FIGS. 5 and 6, a casing 10 is mounted for rotation on fixed coaxial shafts 12a and 12b integral with an internal member 14. The casing 10 is conveniently built up of a casing body 11 and end walls 110 and 11b, The body 11 has an internal peripheral surface following a sinuous profile defining three evenly spaced outwardly extending similar chambers 16, interposed by inwardly extending cam surfaces 18.

The internal member 14 has a body 13 with a circular periphery 17. which latter is in constant sliding contact with the cam surfaces 18. and has a diametral slot 19in which slot a single vane is slidably fitted.

The contour of the profile surface 15 is such that the distance between diametrically opposed profile surfaces is constant. Thus the single vane 20, which is of fixed length corresponding to the said constant distance, will, at each end, contact the profile surface 15 at all positions of rotation of the casing 10.

Upon rotation ofthe casing 10, while one end of the vane 20 sweeps a chamber 16 the other end ofthe vane will ride over a cam surface 18. sliding in the slot 19 in the process, and while the other end of the vane 20 sweeps a succeeding chamber 16 the one end of the vane will ride over a succeeding cam surface 18, and so on to provide continuous displacement of fluid in the chambers.

Inlet ports 22, adjacent to and on the trailing side of the vane 20, connect with passages 24. Discharge ports 26, adjacent to and on the leading side of the vane, connect with passages 28, in the internal member 14.

Conveniently the fixed shafts 12a and 12b are hollow and so cored that the inlet passages 24 lead from one of the hollow shafts, for example 12a connected to a supply of fluid, and the discharge passage 28 lead to the other of the hollow shafts 12b for connection to a delivery line.

The fixed shafts 12a, 12b, may be mounted in any suitable manner, such as on a frame 30.

Any convenient drive means for the casing 10 may be employed, such as by V-belt operating in the groove 32 and driven by an electric motor or other power source, not shown.

Conventional sealing rings 33 and 34 are inserted as indicated.

FIGS. 7 and 8 depict a preferred embodiment of the invention incorporating a novel lateral sealing means to be further described later.

In this design the vane 120 consists of two equal, radially extending parts 120a and 120b, stressed apart by a resilient packer 36. This packer 36 is preferably in the form of a rubber or thermoplastic rod or tube extending the full width of the vane 120, which packer when compressed takes an oval crosssectional shape as shown at 36 in FIG. 7.

The packer 36 serves to resiliently urge the ends of the vane parts 120a, 120b, respectively, against the inner profile 115 of the casing to ensure good sealing contact therebetween and automatically compensate for wear.

The casing 110 is build up of four members, viz a primary end Wall 1110, a casing body 111, a spacer ring 40, and a primary end wall 1 1 1b.

The internal member 114 has a hollow shaft 112a. communicating with inlet passages 124 leading to inlet ports 122 for supply of fluid to the chambers 116. The body 113 of internal member 114 is provided with a flange 42, which constitutes a secondary end wall and conveniently is integral with or attached to a lateral face of the body 113 adjacent to, but spaced from, primary end wall 1l1b by an annular chamber 44.

The spacer ring 40 has an interior circumferential recess 46 to slidingly receive a peripheral portion 43 of the flange 42. This recess extends into a small matching rebate 48 in the casing body 111 to provide a degree of axial freedom for the cats ing relative to the flange 42 and the internal member 114.

The internal member 114 has a hollow outlet shaft [12h communicating with the annular chamber 44 by way of holes 50, and the annular chamber 44 is in fluid communication with the pressure side of the machine by way of ports 52. Thus the annular chamber 44 is subject to continuous hydrostatic pressure which varies directly as the fluid pressure generated by the machine.

In operation the combined internal member 114 and secondary end wall 42 act as a differential piston, as hereinbefore explained, and the casing 110, having limited axial freedom of movement, is free to move axially on the shafts 112a, l12b of the stationary internal member 114 so that the differential hydrostatic pressure acts to press the inner surface of the primary end wall 111a continuously against the adjacent lateral surface of the body 113 of the internal member 114, thereby effecting a pressure contact seal between these lateral surfaces irrespective ofwear that may take place in this region.

In one optional form of construction, shown in FIGS. 9 and 10, the invention provides a novel sealing device between the profile surface of the casing body and the contacting ends of the vane, which device is particularly applicable where a single vane offixed length is employed.

This sealing device comprises a thin liner 60 of resilient sheet material, located within the casing body 211, adjacent the profile surface 215 and conforming to the contour of the profile, the liner being separated from the profile face 215 by a layer 62 of elastic material, such as rubber or synthetic plastic.

For light duty operation, the liner 60 could be made of nylon or other suitable plastic; for heavier duty, spring brass or stainless steel would be suitable.

It is to be understood that the vane (not shown) will be of such proportions and so stressed against the liner 60 that the latter is slightly distorted by the vane at all times, this distortion following the movement of the vane and ensuring good sealing between the vane ends and the liner. With such an arrangement a single diametral vane of fixed length can be conveniently employed, the resilient liner 60, backed by the elastic layer 62, providing adequate and continuous sealing therebetween. It also automatically compensates for wear.

The thickness and nature of the layer 62 can be determined according to the class of work to be performed. However, to prevent the liner 60 from distorting unduly under internal pressure, thereby separating the liner from the vane, stop means may be provided. Such stop means could take the form of inserts of strips or bands 64 on nonelastic material interspersed in the elastic layer 62, but of lesser thickness than the layer, thereby limiting the movement of the liner 60 into the layer 62.

FIGS. 11 and 12 illustrate an alternative arrangement of the invention in which the external member is in the form ofa casing 210 having a circular internal peripheral surface 217, while the internal member 214 has an external peripheral surface following avsinuous profile 215 defining three evenly spaced inwardly extending similar chambers 216 interposed by three outwardly extending cam surfaces 218. Two diametrally opposed vanes 220a and 22b are slidably mounted in the casing 210, said vanes being connected so that they operate in unison. FIG. 12 shows schematically one way of connecting the two vanes 220a and 220b, for example by an external rigid link 250.

The provision of a separate liner, as above described, simplifies construction very considerably since the profile surface of the casing body, not being contacted by the vane, need not be highly finished. Modern shell moulding techniques applied to the casting of the casing body would produce a profile delineation of sufficient accuracy to obviate subsequent machining.

lclaim:

1. A vane-type rotary fluid displacing apparatus; comprising, an external member and an internal member relatively rotatable about a common axis, said external member having an internal peripheral surface and said internal member having an external peripheral surface, said peripheral surface of one of said members having a circular profile and said peripheral surface of the other of said members having a sinuous profile of constant diameter between opposing surfaces thereof, whereby said peripheral surfaces form a plurality of an odd number of evenly spaced chambers interposed by cam surfaces between them; at least one diametrally disposed vane means slidably mounted in said member having a circular profile and having curved ends adapted to continuously contact the diametrally opposed surfaces of said member having a sinuous profile and sweep said surfaces of said member having a sinuous profile, whereby said vane slides in said member having a circular profile as a result of one surface of said member having a sinuous profile forcing said vane toward the diametrally opposite surface of said member having a sinuous profile; and inlet and discharge passages leading into and out of each of said chambers, whereby fluid is alternately drawn into and discharged from said chambers by the sweeping action of said vane; said sinuous profile developed in accordance with the formula:

where:

r the radius vector defining the position of a point representing the center of curvature of said vane end and in calculated in accordance with the formula:

the deflection of said radius vector from the point of maximum deflection ofsimple harmonic motion,

a the radial distance from the center of rotation of said members to the nearest point of simple harmonic motion,

h the radial distance from the center of rotation of said members to the mean position of simple harmonic motion of said point representing the center of curvature ofsaid vane end, and

0 the angle between said radius vector and the tangent to said sinuous profile.

2. Apparatus in accordance with claim 1 wherein the sinuous profile is developed in accordance with the following formula to take into consideration the radius of curvature of the vane end:

where:

r the radius vector defining the position of a second point on a line perpendicular to the tangent to the sinuous profile developed in accordance with claim 1 and displaced from the point representing the center of curvature of said vane end by a distance equal to the radius of curvature of said vane end,

L the deflection of radius vector r,, and

R said radius of curvature of said vane end.

3. Apparatus in accordance with claim 2 wherein the sinuous profile is modified to allow for a liner inside member having a sinuous profile by substituting R+t for R in the formula ofclaim 2, wherein:

t= the thickness of said liner.

4. A machine according to claim 1, wherein the external member is in the form of a casing and has a circular internal peripheral surface, while the internal member has an external peripheral surface following a sinuous profile defining three evenly spaced inwardly extending chambers interposed by three outwardly extending carn surfaces, there being two diametrally opposed vanes slidably mounted in the casing, said two vanes being connected so that they operate in unison.

5. A machine according to claim 4, wherein the casing comprises a body portion and two primary end walls rigid with said body portion and two primary said end walls having inner lateral surfaces opposed to lateral surfaces of the internal member operating within said casing, characterized by pressure-assisted sealing means for relatively moving contacting faces of said lateral surfaces, said sealing means comprising a secondary end wall disposed against or integral with one lateral surface of said internal member and defining an annular space between said secondary end wall and one of said primary end walls, the internal member and secondary end wall having limited freedom of axial movement relative to said casing, said space being utilized to apply fluid pressure between said secondary end wall and said one of said primary end walls thereby pressing the other lateral surface of said internal member against the other of said primary end walls to provide a pressure-assisted seal at said relatively moving contacting faces of said lateral surfaces.

6. A machine according to claim 5, wherein the fluid pressure generated by the machine is employed to provide said fluid pressure-assisted sealing by means of ducting affording fluid communication between said space and the discharge (pressure) side of the machine.

7. A machine according to claim 1, wherein the external member is in the form of a casing and has an internal peripheral surface following a sinuous profile defining three. evenly spaced outwardly extending chambers interposed by three inwardly extending cam surfaces, the internal member being circular and having a diametrally disposed vane slidably mounted therein and adapted to continuously contact and sweep the casing profile.

8. A machine according to claim 7, wherein the internal member is stationary and comprised ofa circular body portion having a shaft extending axially from each end of said body portion, the axis of the shafts being coincident with the center of the circular body portion and said shafts being hollow, one of the hollow shafts serving as inlet means to the inlet passages of the machine and the other of the hollow shafts serving as outlet means from the discharge passages of the machine.

9. A machine according to claim 7, wherein the diametral vane is composed of two equal, radially extending portions stressed apart by resilient means so that profile-contacting edges of the vane portions are constantly pressed against the profile surface to improve sealing.

10. A machine according to claim 9, wherein the resilient means comprises a rubber or synthetic plastic tube or rod extending transversely of the vane for the width of the vane.

11. A machine according to claim 7, and including a sealing device between the casing profile surface and the vane, which sealing device comprises a thin liner of resilient sheet material located within the casing adjacent the profile surface and connal pressure, said stop means comprising inserts of strips or bands of nonelastic material interspersed in the elastic layer but of lesser thickness than the layer, thereby limiting movement of the liner into the layer. 

1. A vane-type rotary fluid displacing apparatus; comprising, an external member and an internal member relatively rotatable about a common axis, said external member having an internal peripheral surface and said internal member having an external peripheral surface, said peripheral surface of one of said members having a circular profile and said peripheral surface of the other of said members having a sinuous profile of constant diameter between opposing surfaces thereof, whereby said peripheral surfacEs form a plurality of an odd number of evenly spaced chambers interposed by cam surfaces between them; at least one diametrally disposed vane means slidably mounted in said member having a circular profile and having curved ends adapted to continuously contact the diametrally opposed surfaces of said member having a sinuous profile and sweep said surfaces of said member having a sinuous profile, whereby said vane slides in said member having a circular profile as a result of one surface of said member having a sinuous profile forcing said vane toward the diametrally opposite surface of said member having a sinuous profile; and inlet and discharge passages leading into and out of each of said chambers, whereby fluid is alternately drawn into and discharged from said chambers by the sweeping action of said vane; said sinuous profile developed in accordance with the formula: tan phi r1d theta /dr1 where: r1 the radius vector defining the position of a point representing the center of curvature of said vane end and in calculated in accordance with the formula: r1 b+(b-a) cos 3 theta , theta the deflection of said radius vector from the point of maximum deflection of simple harmonic motion, d theta /dr1 -3(b-a) sin 3 theta , a the radial distance from the center of rotation of said members to the nearest point of simple harmonic motion, b the radial distance from the center of rotation of said members to the mean position of simple harmonic motion of said point representing the center of curvature of said vane end, and theta the angle between said radius vector and the tangent to said sinuous profile.
 2. Apparatus in accordance with claim 1 wherein the sinuous profile is developed in accordance with the following formula to take into consideration the radius of curvature of the vane end: where: r2 the radius vector defining the position of a second point on a line perpendicular to the tangent to the sinuous profile developed in accordance with claim 1 and displaced from the point representing the center of curvature of said vane end by a distance equal to the radius of curvature of said vane end, Iota the deflection of radius vector r2, and R said radius of curvature of said vane end.
 3. Apparatus in accordance with claim 2 wherein the sinuous profile is modified to allow for a liner inside member having a sinuous profile by substituting R+t for R in the formula of claim 2, wherein: t the thickness of said liner.
 4. A machine according to claim 1, wherein the external member is in the form of a casing and has a circular internal peripheral surface, while the internal member has an external peripheral surface following a sinuous profile defining three evenly spaced inwardly extending chambers interposed by three outwardly extending cam surfaces, there being two diametrally opposed vanes slidably mounted in the casing, said two vanes being connected so that they operate in unison.
 5. A machine according to claim 4, wherein the casing comprises a body portion and two primary end walls rigid with said body portion and two primary said end walls having inner lateral surfaces opposed to lateral surfaces of the internal member operating within said casing, characterized by pressure-assisted sealing means for relatively moving contacting faces of said lateral surfaces, said sealing means comprising a secondary end wall disposed against or integral with one lateral surface of said internal member and defining an annular space between said secondary end wall and one of said primary end walls, the internal member and secondary end wall having limited freedom of axial movement relative to said casing, said space being utilized to apply fluid pressure between said secoNdary end wall and said one of said primary end walls thereby pressing the other lateral surface of said internal member against the other of said primary end walls to provide a pressure-assisted seal at said relatively moving contacting faces of said lateral surfaces.
 6. A machine according to claim 5, wherein the fluid pressure generated by the machine is employed to provide said fluid pressure-assisted sealing by means of ducting affording fluid communication between said space and the discharge (pressure) side of the machine.
 7. A machine according to claim 1, wherein the external member is in the form of a casing and has an internal peripheral surface following a sinuous profile defining three evenly spaced outwardly extending chambers interposed by three inwardly extending cam surfaces, the internal member being circular and having a diametrally disposed vane slidably mounted therein and adapted to continuously contact and sweep the casing profile.
 8. A machine according to claim 7, wherein the internal member is stationary and comprised of a circular body portion having a shaft extending axially from each end of said body portion, the axis of the shafts being coincident with the center of the circular body portion and said shafts being hollow, one of the hollow shafts serving as inlet means to the inlet passages of the machine and the other of the hollow shafts serving as outlet means from the discharge passages of the machine.
 9. A machine according to claim 7, wherein the diametral vane is composed of two equal, radially extending portions stressed apart by resilient means so that profile-contacting edges of the vane portions are constantly pressed against the profile surface to improve sealing.
 10. A machine according to claim 9, wherein the resilient means comprises a rubber or synthetic plastic tube or rod extending transversely of the vane for the width of the vane.
 11. A machine according to claim 7, and including a sealing device between the casing profile surface and the vane, which sealing device comprises a thin liner of resilient sheet material located within the casing adjacent the profile surface and conforming to the contour of the profile, the liner being separated from the profile face by a layer of elastic material, such as rubber or resilient plastic.
 12. A machine according to claim 11, and including stop means to prevent the liner from distorting unduly under internal pressure, said stop means comprising inserts of strips or bands of nonelastic material interspersed in the elastic layer but of lesser thickness than the layer, thereby limiting movement of the liner into the layer. 